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Lower-dimensional decompositions using complex variables
Archivum mathematicum, Tome 34 (1998) no. 3, pp. 329-336 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The purpose of the present paper is to represent non-holomorphic functions depending on one or several complex variables by holomorphic and anti-holomorphic functions depending on only one complex variable. Similarly as in the case of functions of real variables, the obtained criteria can also be interpreted as conditions for the solvability of functional equations.
The purpose of the present paper is to represent non-holomorphic functions depending on one or several complex variables by holomorphic and anti-holomorphic functions depending on only one complex variable. Similarly as in the case of functions of real variables, the obtained criteria can also be interpreted as conditions for the solvability of functional equations.
Classification : 30D05, 30G20, 39B32
Keywords: holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain 
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     url = {http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a0/}
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Tutschke, Wolfgang. Lower-dimensional decompositions using complex variables. Archivum mathematicum, Tome 34 (1998) no. 3, pp. 329-336. http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a0/

[1] Balk M. B.: Polyanalytic functions. Akademie-Verlag Berlin 1991. | MR | Zbl

[2] Čadek M., Šimša J.: Decomposable functions of several variables. Aequat. Mathem., vol.40, 1990, 8-25. | MR

[3] Čadek M., Šimša J.: Decompositions of smooth functions of two multidimensional variables. Czechoslovak Mathem. Journ., vol. 41 (116) 1991, 342-358. | MR

[4] Gauchman H., Rubel L. A.: Sums of products of functions of $x$ times functions of $y$. Linear Algebra Appl., vol. 125, 1989, 19-63. | MR | Zbl

[5] Herold H.: Differentialgleichungen im Komplexen. Göttingen 1975. | MR | Zbl

[6] Hörmander L.: Introduction to Complex Analysis in Several Variables. | Zbl

[7] Neuman F.: Functions of two variables and matrices involving factorizations. C. R. Math. Rep. Acad. Sci. Canada, vol. 3, 1981, 7-11. | MR | Zbl

[8] Neuman F.: Factorizations of matrices and functions of two variables. Czechoslovak Math. Journ., vol. 32, 1982, 582-588. | MR | Zbl

[9] Neuman F.: Finite sums of products of functions in single variables. Linear Algebra Appl., vol. 134, 1990, 153-164. | MR | Zbl

[10] Neuman F., Rassias, Th. M.: Functions decomposable into finite sums of products (old and new results, problems and trends). Contained in the volume Constantin Caratheodory: An International Tribute (ed. by Th. M. Rassias), 956-963, World Scientific Publ. Co. 1991. | MR | Zbl

[11] Rassias, Th. M., Šimša J.: Finite sums decompositions in Mathematical Analysis. Wiley, Chichester 1995. | MR | Zbl

[12] Schwartz L.: Théorie des distributions. Tome I, Paris 1957. | Zbl

[13] Šimša J.: Some factorizations of matrix functions in several variables. Arch. Math.(Brno), vol. 28, 1994, 85-94. | MR

[14] Tutschke W.: Partielle Differentialgleichungen. Klassische, funktionalanalytische und komplexe Methoden. Teubner-Text Bd. 27, Leipzig 1983. | MR | Zbl

[15] Tutschke W., Withalm C.: Nonholomorphic solutions to ordinary differential equations in the complex domain. Math. Nachr., vol. 144, 1989, 109-117. | MR

[16] Vekua I. N.: New methods for solving elliptic equations. Wiley, New York 1967. | MR | Zbl

[17] Vekua I. N.: Generalized analytic functions. 2nd edit. Moscow 1988 (in Russian); Engl. transl. Oxford 1962. | MR | Zbl